bands

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Bands

Definition

A \emph{band} is a semigroup $\mathbf{B}=\langle B,\cdot \rangle$ such that

$\cdot$ is idempotent: $x\cdot x=x$ .

Morphisms

Let $\mathbf{B}$ and $\mathbf{C}$ be bands. A morphism from $\mathbf{B}$ to $\mathbf{C}$ is a function $h:B\to C$ that is a homomorphism: $h(xy)=h(x)h(y)$

Examples

Basic results

Properties

Classtype	variety
Equational theory	decidable in polynomial time
Quasiequational theory
First-order theory
Locally finite	yes
Residual size
Congruence distributive	no
Congruence modular	no
Congruence n-permutable	no
Congruence regular	no
Congruence uniform	no
Congruence extension property	no
Definable principal congruences
Equationally def. pr. cong.
Amalgamation property	no
Strong amalgamation property	no
Epimorphisms are surjective